Open 21

Open 21 is a new blackjack/double exposure variant by our own MrCasinoGames. There is already some discussion of it in the 2016. NEW TABLE GAMES SHOWCASE thread. However, it is mixed in with discussion of other games. I think after posting a page on the game, it is worthy of its own thread.

So, please visit my new page on Open 21. As always, I welcome questions, comments, and especially corrections.

The question for the poll is would you play Open 21, assuming the house edge was the same as regular blackjack? Which other statements do you agree with?

My first thought is there is too much going on. With the changes in strategy based on the side bet, I don't see too many people taking the time to learn near perfect play. So it comes down to will the average player find this more "fun" than basic BJ and fall into Carnival game territory. I don't see that either. Maybe some will try it based on the thought that they have an advantage seeing both cards, like Stupak did 30 years ago. Just my thoughts.

Quote: Boz

My first thought is there is too much going on. With the changes in strategy based on the side bet, I don't see too many people taking the time to learn near perfect play. So it comes down to will the average player find this more "fun" than basic BJ and fall into Carnival game territory. I don't see that either. Maybe some will try it based on the thought that they have an advantage seeing both cards, like Stupak did 30 years ago. Just my thoughts.

Way too many things going on. Likely the dealers will kill this.

Agree with the two above posts. Now that we know the gimmick, it's going to be a tough sell. Good luck with it though Stephen.

P.S. I'd play it if I can find a sucker, err someone to make the odds win bet for me :-D

I can work this out (but since the math is already done), how often does the player lose the Odds bet after the initial deal (e.g. the frequency of an even initial two card total)?

I can't see dealers supporting this game, as dealers either quietly support a game, or quietly sabotage a game. If dealers don't have fun dealing a game, the gamblers won't have fun playing it with the dealers.

The other thing is that the new features (in the odds bet) are very non-blackjack-like, in the sense that they're alien add-ons to the game: the odds bet wins if you win the hand with an odd total in your first two cards, but lose if you win the hand with [an even total in your first two cards. Dealer and player alike now have to think: "your odd 19 final hand had started with an even 12, so your winning 19 loses the odds bet in this case...." and the like.

I liked Deal and Reveal, as it helped strategy by knowing what the dealer has with a stiff upcard without adding an odd-or-even strategy wrench into the mix. A good humdinger adds game juice without adding game complexity or additional work.

Quote: Paigowdan

I can't see dealers supporting this game, as dealers either quietly support a game, or quietly sabotage a game. If dealers don't have fun dealing a game, the gamblers won't have fun playing it with the dealers.

The other thing is that the new features (in the odds bet) are very non-blackjack-like, in the sense that they're alien add-ons to the game: the odds bet wins if you win the hand with an odd total in your first two cards, but lose if you win the hand with [an even total in your first two cards. Dealer and player alike now have to think: "your odd 19 final hand had started with an even 12, so your winning 19 loses the odds bet in this case...." and the like.

I liked Deal and Reveal, as it helped strategy by knowing what the dealer has with a stiff upcard without adding an odd-or-even strategy wrench into the mix. A good humdinger adds game juice without adding game complexity or additional work.

I agree. The concept of winning and losing the odds bet base on starting with an odd or even hand total is silly.

Quote: Paigowdan

I can't see dealers supporting this game, as dealers either quietly support a game, or quietly sabotage a game. If dealers don't have fun dealing a game, the gamblers won't have fun playing it with the dealers.

The other thing is that the new features (in the odds bet) are very non-blackjack-like, in the sense that they're alien add-ons to the game: the odds bet wins if you win the hand with an odd total in your first two cards, but lose if you win the hand with [an even total in your first two cards. Dealer and player alike now have to think: "your odd 19 final hand had started with an even 12, so your winning 19 loses the odds bet in this case...." and the like.

I liked Deal and Reveal, as it helped strategy by knowing what the dealer has with a stiff upcard without adding an odd-or-even strategy wrench into the mix. A good humdinger adds game juice without adding game complexity or additional work.

The odds bet is resolved before the player starts taking hits,so I don't think it will be that confusing.

True, my bad: if the first two cards have an even total, the odds bet can/is taken at the start of the hit-or-stand phase, but this exposes the frequent losses up front by adding an additional "take the losers" step against the players.

While this makes dealing it easier, if it were done later at the take-and-pay stage, the losing "even-start" odds bet would be masked a bit on a hand result win: win the main bet, and sneak-away the odds bet loss. You'd skip this "lose only" action at the start of the round. If a player starts with an even hand and loses the odds bet to the dealer, and later loses his hand to the dealer, he now gets two losing actions in one round of play. Combining the even-start odds bet loss into one final take-and-pay action may hide it somewhat, since a main bet win covers the odds bet loss in these cases. I'm just looking at the mechanism in a "juice look" view over here, in which game designers should try to conceal the house's edge: promote the player-friendly gimmick while concealing he house's taking hand as much as possible.

Either way, the odds bet house edge is hard to conceal, whether the odds is taken upfront at the hit-or-stand point, or at the take-and-pay point, because it is not based on the win/loss result of the hand.

In Double Exposure Blackjack, which has the same open dealer hand mechanism, you also lose on ties, but this happens in one step during take-and-pay with no forced (and frequently losing) prop bet.

In looking at BJ house edge mechanisms, Geoff Hall's Push-22 is as soft as they come, if you look at the installs. An iron fist should be cloaked in a velvet glove when it comes to house edge mechanisms.

Mandated side bet = bad... especially because you have to win twice to win it... have to get an odd hand THEN you have to win the BJ hand.

P(odd hand) = P(getting 1 odd and 1 even card) = P(odd) * P(even) = (5/13) * (8/13) = .3846 * .6154 = .2367 = 23.67% chance of getting an odd hand.

THEN

You have to win the BJ hand. Assuming "similar" figures to regular BJ (the auto 21 win would change the numbers 'barely' perhaps) but the player is going to win 42%, push 9%, and lose 49%... So the player needs to also hit one of his "winning" hands (42% of the time). Then again, I don't know the odds on double exposure win rate off the top of my head, so actually this is probably a bit higher.*

So in order to not lose half the value of your main bet (aka win the side bet) you need to P(odd hand) * P(Winning Blackjack Hand) = .2367 * .42 = .0994.

Am I correct that the player will win the BJ AND the side bet only ~9.94% of the time? That sounds like ZERO fun to always be losing something 90% of the time.

*Edit: Numbers will change a bit for double exposure win rate, but I'd still think it comes out to quite a low number (<20%) to actually win both bets.

Yup, looks rough.

The house edge is low, and as such is fine for BJ type games, - but it is the feel of the game, the "Gambler's GFE" that counts.

Quote: Romes

....P(odd hand) = P(getting 1 odd and 1 even card) = P(odd) * P(even) = (5/13) * (8/13) = .3846 * .6154 = .2367 = 23.67% chance of getting an odd hand...

Your other points are also valid, but to me the worst "feel" of this game is going to be losing this mandatory side bet 75%+ of hands right after the initial deal with a maximum upside on the win of 2-1.

Quote: Wizard

Open 21...I welcome questions, comments, and especially corrections...

When I analysed it quickly using infinite deck I recall there were only two squares where the strategy depended on whether you had an Odds bet still running. So it might be easier to have one strategy card. Note that I separated hitting from Doubling - the latter knows whether you've started Even or Odd!

(i) There seems to be a misalignment in the Basic Strategy For Even Starting Hands s17 as the double 11 row is marked 13.
(ii) I think it's worth mentioning whether you split or double with (say) 3,3 vs 16 or similar.
(iii) The rules state the dealer stands on Soft 17 - so there's an argument to leave out that bit (or just say this is only in the UK at the moment).
(iv) 17-21 could be handled as "Stiffs" catering for both hard and soft totals where the final dealer's total is known (although I can see card dependent strategies may be different if there were any close decisions).
Note : I haven't checked my strategy and it comes out with a different House Edge, so there's probably something that I've missed.

Quote: Hunterhill

The odds bet is resolved before the player starts taking hits,so I don't think it will be that confusing.

Hi Hunterhill,

Thanks for pointing this out.

Open 21® Blackjack is very Easy and Simple. Just follow the 4 Simple steps (Dealing Procedures) as show below:

1. Each Player must make both a main wager and an Odds-Win wager equal to half his main wager.

2. Each Player and the Dealer receives two cards (All Face-up).

3. If the Player’s two-card hand total is Even then his Odds-Win wager loses; otherwise it remains in play.

4. Play continues as normal Blackjack and the Odds-Win wager (if any) is resolved in the following way:
a. If the Player wins on his hand, his Odds-Win wager (if any) wins 2 to 1.
b. If the Player pushes on his hand, his Odds-Win wager (if any) will push.
c. If the Player loses on his hand, his Odds-Win wager (if any) loses.

I don't like forced side bets. And it seems too complex. Count me out.

Quote: Rule 7

If the player draws or doubles to 21 points, it shall be an immediate winner and pay 1-1.

Even if the dealer has a natural 21?

Quote: DJTeddyBear

Even if the dealer has a natural 21?

Yes, Even if the dealer has a natural 21 (Blackjack).

Quote: Paradigm

Your other points are also valid, but to me the worst "feel" of this game is going to be losing this mandatory side bet 75%+ of hands right after the initial deal with a maximum upside on the win of 2-1.

Hi Paradigm,

The Probability of a Odd Total on the initial 2 card dealt in a 6-Deck game is 47.4895%.
Notes: (An odd number + even number = odd number) or (A even number + an odd number = odd number).

Quote: DJTeddyBear

...Even if the dealer has a natural 21?

The players and dealer will see the dealer's natural 21 as soon as it is dealt, and thus the dealer will not allow any player to take hits or double-down.

Edit: I defer to Mr. Casino Games on this one. The dealer's natural is just counted as a regular 21, and will be beaten by players' 21s.

Quote: ChesterDog

The players and dealer will see the dealer's natural 21 as soon as it is dealt, and thus the dealer will not allow any player to take hits or double-down.

Hi ChesterDog,

In Open 21® Blackjack:

* A Dealer’s two-card total of 21 does not count as a natural blackjack, and only acts as an ordinary total of 21; the player will still be able to play out their hand.

* Any other player total of 21 (including after hitting, splitting and/or doubling) pays at a rate of 1:1 and wins against any dealer hand.

Quote: MrCasinoGames

Hi Paradigm,

The Probability of a Odd Total on the initial 2 card dealt in a 6-Deck game is 47.4895% (Notes: An odd number + even number = odd number).

Thanks MCG, I was going off of Romes calculation above. His number is about 1/2 of your number and makes me think he didn't consider that order of whether an Odd or Even card comes first is irrelevant...so should his calculation should be multiplied by 2? This is a better number than his for sure ;-).

Quote: charliepatrick

When I analysed it quickly using infinite deck I recall there were only two squares where the strategy depended on whether you had an Odds bet still running. So it might be easier to have one strategy card. Note that I separated hitting from Doubling - the latter knows whether you've started Even or Odd!

You're right, there are very few differences. I'm surprised.

Quote:

(i) There seems to be a misalignment in the Basic Strategy For Even Starting Hands s17 as the double 11 row is marked 13.

You're right. Thanks for the correction. I just fixed it.

Quote:

(ii) I think it's worth mentioning whether you split or double with (say) 3,3 vs 16 or similar.

I'm not sure I see your point. D=double and P = split. They are also in different colors.

Quote:

(iii) The rules state the dealer stands on Soft 17 - so there's an argument to leave out that bit (or just say this is only in the UK at the moment).

Good point. I just eliminated that last rule about standing on soft 17, although that is the case with all placements so far.

Quote:

(iv) 17-21 could be handled as "Stiffs" catering for both hard and soft totals where the final dealer's total is known (although I can see card dependent strategies may be different if there were any close decisions).

Are you suggesting I just say those cases are obvious and leave them off the table? If I go down that road, people will ask me why I list obvious plays in the blackjack tables. I do because if I don't, people will write to me asking how to play hands like a hard 20 in blackjack.

Quote:

Note : I haven't checked my strategy and it comes out with a different House Edge, so there's probably something that I've missed.

MrCasinoGames was kind enough to give me his spreadsheet. You might ask him if you can have a copy, if the differences are keeping you up at night.

Quote: charliepatrick

When I analysed it quickly using infinite deck I recall there were only two squares where the strategy depended on whether you had an Odds bet still running. So it might be easier to have one strategy card. Note that I separated hitting from Doubling - the latter knows whether you've started Even or Odd!

(i) There seems to be a misalignment in the Basic Strategy For Even Starting Hands s17 as the double 11 row is marked 13.
(ii) I think it's worth mentioning whether you split or double with (say) 3,3 vs 16 or similar.
(iii) The rules state the dealer stands on Soft 17 - so there's an argument to leave out that bit (or just say this is only in the UK at the moment).
(iv) 17-21 could be handled as "Stiffs" catering for both hard and soft totals where the final dealer's total is known (although I can see card dependent strategies may be different if there were any close decisions).
Note : I haven't checked my strategy and it comes out with a different House Edge, so there's probably something that I've missed.

Hi charliepatrick,

Thanks for your inputs.

PM me if you would like a copy of the spreadsheet and report (By Charles R. Mousseau) on Open 21® Blackjack.

Quote: MrCasinoGames

Hi Paradigm,

The Probability of a Odd Total on the initial 2 card dealt in a 6-Deck game is 47.4895%.
Notes: (An odd number + even number = odd number) or (A even number + an odd number = odd number).

Ah, my apologies for only doing half the equation...

P(Odd Hand) = P(1stOdd 2ndEven) + P(1stEven 2ndOdd)

P(1stOdd 2ndEven) = 23.67%

HOWEVER

P(1stEven 2ndOdd) = 23.67%

Thus, P(Odd Hand) = 23.67% + 23.67% = 47.34%

...Though, you still have to ALSO win the BJ hand to actually win the bet... Thus P(Winning Side Bet) = .4734 * .42 = .1988... So you lose the side bet 4/5 times, it's mandatory, and the big upside is a 2-1 pay on that 20% of the time (assuming you play proper basic strategy and don't have a higher loss rate in BJ).

Quote: Romes

*Edit: Numbers will change a bit for double exposure win rate, but I'd still think it comes out to quite a low number (<20%) to actually win both bets.

Hey I still wasn't that far off lol.

Quote: Romes

Ah, my apologies for only doing half the equation...

P(Odd Hand) = P(1stOdd 2ndEven) + P(1stEven 2ndOdd)

P(1stOdd 2ndEven) = 23.67%

HOWEVER

P(1stEven 2ndOdd) = 23.67%

Thus, P(Odd Hand) = 23.67% + 23.67% = 47.34%

...Though, you still have to ALSO win the BJ hand to actually win the bet... Thus P(Winning Side Bet) = .4734 * .42 = .1988... So you lose the side bet 4/5 times, it's mandatory, and the big upside is a 2-1 pay on that 20% of the time (assuming you play proper basic strategy and don't have a higher loss rate in BJ).

Quote: Romes

*Edit: Numbers will change a bit for double exposure win rate, but I'd still think it comes out to quite a low number (<20%) to actually win both bets.

Hey I still wasn't that far off lol.

Hi Romes,
Thanks for your update.

Quote: Wizard

...the differences are keeping you up at night...

Yes I'm still getting sleepless nights!

Side Bet probabilities

Running various simulations it seems the House Edge is lower for six decks than infinite decks and the side bet came out..

Even or Odd	Win/Lose	Percent
Even	Lose	52.52%
Odd	Win	23.32%
Odd	Tie	3.70%
Odd	Lose	20.47%

Splitting Tens rules

I also seem to get that the rule for splitting tens has a fair influence on the House Edge whether
(i) you can split any two ten-valued cards or just ranked pairs (e.g. KK KQ KJ...TT or just KK QQ JJ TT)
(ii) you can resplit any many times as you wish
(iii) you can double if you receive an Ace on a picture card (I suspect Grosvenor will use their you can't double 21 rule).

Strategy e.g. vs 16 and other stiffs

When the dealer has 16 in normal Double Exposure you pile on money, for instance double 5 or 6 or any soft value ( https://wizardofodds.com/games/double-exposure/ ) so I should have expected the same. The only difference is with a starting odd total you also don't want to seriously affect the chances of the Side Bet winning, so you would't double 5 if that's your initial score but do if it's been created after a split. However you would always double 6 (2-4 not 3-3) vs 16 as the Side Bet has gone.

Thus I get it (infinite deck) that you are more aggressive with doubling and splitting.

Quote: charliepatrick

Yes I'm still getting sleepless nights!

Side Bet probabilities

Running various simulations it seems the House Edge is lower for six decks than infinite decks and the side bet came out..

Even or Odd	Win/Lose	Percent
Even	Lose	52.52%
Odd	Win	23.32%
Odd	Tie	3.70%
Odd	Lose	20.47%

Splitting Tens rules

I also seem to get that the rule for splitting tens has a fair influence on the House Edge whether
(i) you can split any two ten-valued cards or just ranked pairs (e.g. KK KQ KJ...TT or just KK QQ JJ TT)
(ii) you can resplit any many times as you wish
(iii) you can double if you receive an Ace on a picture card (I suspect Grosvenor will use their you can't double 21 rule).

Strategy e.g. vs 16 and other stiffs

When the dealer has 16 in normal Double Exposure you pile on money, for instance double 5 or 6 or any soft value ( https://wizardofodds.com/games/double-exposure/ ) so I should have expected the same. The only difference is with a starting odd total you also don't want to seriously affect the chances of the Side Bet winning, so you would't double 5 if that's your initial score but do if it's been created after a split. However you would always double 6 (2-4 not 3-3) vs 16 as the Side Bet has gone.

Thus I get it (infinite deck) that you are more aggressive with doubling and splitting.

Hi charliepatrick,

Thanks for your input.

You have been given very helpful and great info on Open 21® Blackjack.

Hi, I saw your post just now and it said the house edge is 0.5%, could you show the probabilities of the odds win and the main bet, thank you